Year 10 Simultaneous Equations Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 10 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Simultaneous EquationsYear 10 Simultaneous Equations Worksheet — Level 1 — Practice Set 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: x + 2y = 0 and x − 2y = 12
Answer: x = 6, y = −3
- Subtract equation 2 from equation 1: 4y = −12
- y = −3
- Substitute into equation 1: x − 6 = 0, so x = 6
2.Solve simultaneously: x + 2y = −2 and x − y = 13
Answer: x = 8, y = −5
- Subtract equation 2 from equation 1: 3y = −15
- y = −5
- Substitute into equation 1: x − 10 = −2, so x = 8
3.Solve simultaneously: x + 4y = −18 and x − 4y = 14
Answer: x = −2, y = −4
- Subtract equation 2 from equation 1: 8y = −32
- y = −4
- Substitute into equation 1: x − 16 = −18, so x = −2
4.Solve simultaneously: x + 3y = 25 and x − 3y = −17
Answer: x = 4, y = 7
- Subtract equation 2 from equation 1: 6y = 42
- y = 7
- Substitute into equation 1: x + 21 = 25, so x = 4
5.Solve simultaneously: x + y = 6 and x − y = 8
Answer: x = 7, y = −1
- Subtract equation 2 from equation 1: 2y = −2
- y = −1
- Substitute into equation 1: x − 1 = 6, so x = 7
6.Solve simultaneously: x + 2y = −8 and x − 4y = 4
Answer: x = −4, y = −2
- Subtract equation 2 from equation 1: 6y = −12
- y = −2
- Substitute into equation 1: x − 4 = −8, so x = −4
7.Solve simultaneously: x + 3y = 0 and x − 3y = −12
Answer: x = −6, y = 2
- Subtract equation 2 from equation 1: 6y = 12
- y = 2
- Substitute into equation 1: x + 6 = 0, so x = −6
8.Solve simultaneously: x + 4y = 7 and x − 4y = −9
Answer: x = −1, y = 2
- Subtract equation 2 from equation 1: 8y = 16
- y = 2
- Substitute into equation 1: x + 8 = 7, so x = −1
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.